Propagation of random errors in R

I have a dataset that contains triplicate measurements of 16 different PAHs (pollutants) in 23 different samples. I would like to calculate the propagated error for the sum of the mean triplicate concentration of the 16 PAHs for each sample. Is there a function that does this in R? Here is the dataset for one of the samples I have:

Q <- biochar %>%   filter(pollutant_class == "PAH",         sample_ID == "WT-BC-700") %>%   select(sample_ID, pollutant, conc)sample_ID              pollutant  conc2  WT-BC-700           Acenaphthene 0.50925 WT-BC-700           Acenaphthene 0.43046 WT-BC-700           Acenaphthene 0.4913  WT-BC-700         Acenaphthylene 3.41026 WT-BC-700         Acenaphthylene 2.99042 WT-BC-700         Acenaphthylene 3.50027 WT-BC-700             Anthracene 1.81036 WT-BC-700             Anthracene 2.09040 WT-BC-700             Anthracene 2.02020 WT-BC-700      Benz(a)anthracene 0.08132 WT-BC-700      Benz(a)anthracene 0.08748 WT-BC-700      Benz(a)anthracene 0.0861  WT-BC-700         Benzo(a)pyrene 0.0788  WT-BC-700         Benzo(a)pyrene 0.0899  WT-BC-700         Benzo(a)pyrene 0.0967  WT-BC-700   Benzo(b)fluoranthene 0.05115 WT-BC-700   Benzo(b)fluoranthene 0.05622 WT-BC-700   Benzo(b)fluoranthene 0.05516 WT-BC-700     Benzo(ghi)perylene 0.02224 WT-BC-700     Benzo(ghi)perylene 0.02234 WT-BC-700     Benzo(ghi)perylene 0.0206  WT-BC-700   Benzo(k)fluoranthene 0.06721 WT-BC-700   Benzo(k)fluoranthene 0.07139 WT-BC-700   Benzo(k)fluoranthene 0.0804  WT-BC-700               Chrysene 0.0935  WT-BC-700               Chrysene 0.09723 WT-BC-700               Chrysene 0.08417 WT-BC-700   Dibenz(ah)anthracene 0.00719 WT-BC-700   Dibenz(ah)anthracene 0.00937 WT-BC-700   Dibenz(ah)anthracene 0.00911 WT-BC-700           Fluoranthene 1.59033 WT-BC-700           Fluoranthene 1.44047 WT-BC-700           Fluoranthene 1.62030 WT-BC-700               Fluorene 0.85041 WT-BC-700               Fluorene 0.87745 WT-BC-700               Fluorene 0.78218 WT-BC-700 Indeno(1,2,3-cd)pyrene 0.03029 WT-BC-700 Indeno(1,2,3-cd)pyrene 0.03343 WT-BC-700 Indeno(1,2,3-cd)pyrene 0.02413 WT-BC-700            Naphthalene 5.62014 WT-BC-700            Naphthalene 4.38044 WT-BC-700            Naphthalene 5.73010 WT-BC-700           Phenanthrene 6.64028 WT-BC-700           Phenanthrene 7.08035 WT-BC-700           Phenanthrene 5.93012 WT-BC-700                 Pyrene 0.98631 WT-BC-700                 Pyrene 1.19038 WT-BC-700                 Pyrene 1.110

I have created a summary table with the mean and standard deviation of each pollutant:

means <- Q %>%   group_by(sample_ID, pollutant) %>%   summarise(mean_conc = mean(conc),            sd_conc = sd(conc))`summarise()` has grouped output by 'sample_ID'. You can override using the`.groups` argument.means # A tibble: 16 × 4# Groups:   sample_ID [1]   sample_ID pollutant              mean_conc sd_conc<chr>     <chr>                      <dbl>   <dbl> 1 WT-BC-700 Acenaphthene             0.477   0.0414  2 WT-BC-700 Acenaphthylene           3.3     0.272   3 WT-BC-700 Anthracene               1.97    0.146   4 WT-BC-700 Benz(a)anthracene        0.0847  0.00321 5 WT-BC-700 Benzo(a)pyrene           0.0877  0.00907 6 WT-BC-700 Benzo(b)fluoranthene     0.054   0.00265 7 WT-BC-700 Benzo(ghi)perylene       0.0213  0.00115 8 WT-BC-700 Benzo(k)fluoranthene     0.0727  0.00666 9 WT-BC-700 Chrysene                 0.0913  0.0066610 WT-BC-700 Dibenz(ah)anthracene     0.00833 0.0011511 WT-BC-700 Fluoranthene             1.55    0.0964 12 WT-BC-700 Fluorene                 0.836   0.0490 13 WT-BC-700 Indeno(1,2,3-cd)pyrene   0.029   0.0045814 WT-BC-700 Naphthalene              5.24    0.750  15 WT-BC-700 Phenanthrene             6.55    0.580  16 WT-BC-700 Pyrene                   1.10    0.103  

And then I created a summary of the total concentration of all the PAHs:

summary <- means %>%   group_by(sample_ID) %>%   summarise(sum_pollutant = sum(mean_conc))summary# A tibble: 1 × 2  sample_ID sum_pollutant<chr>             <dbl>1 WT-BC-700          21.5

So my question is: how can I calculate the propagated error for sum_pollutant in the summary data frame?

I tried finding the answer in the propagate() package, but this got a bit too complex for me and I wasn't sure if this was the right place to look. I would like to use the following expression for the propagated error:

σx = sqrt(σa^2 +σb^2 +σc^2)

a, b, and c are measured variables and σa, σb, and σc are the standard deviations of those variables.